Answer: f(x) = 4*cos(x*2*pi/3)
Where I assumed that the period is 3, instead of 3x
Step-by-step explanation:
In a general equation like:
f(x) = a*cos(b*x)
a is the amplitude.
b is the angular frequency, which is equal to two pi times the inverse of the period.
In this case, we know that the amplitude is 4, then a = 4.
And the period is 3x (i guess that this is wrong because the period should not depend on the variable, as we will see later), then the frequency is:
b = 2*pi/3x
Replacing these in the equation we get:
f(x) = 4*cos(x*2*pi/3x) = 4*cos(2*pi/3)
Then we have no longer a dependence on x.
If the period is equal to 3, then the frequency will be:
b = 2*pi/3
Then the equation now is
f(x) = 4*cos(x*2*pi/3)
This is a cosine function, as we wanted.
